If you invalidate the EEPROM (by shorting an appropriate pin to ground?), does the bridge revert to its generic factory code? It should identify itself as an INIC-3609 rather than a Seagate device.
Thank you very much for the suggestion. While I've read that doing that is possible I haven't tried it yet. The goal is to be able to 'fix' drives with INIC-3609 bridges without having to pry apart the enclosures (which don't always snap together cleanly after disassembly, and I could just swap the bridge boards once they're open anyway).
I made a couple more changes in a hex editor (replacing a suspected location of the VID with the Seagate value and reverting the string to 'INIC-3609' in case the bridge always returns its real name to commands from the flashing software) but no combination has worked yet.
I'm also exploring the possibility that the problem is UASP-related. A number of early controllers and bridges, especially with early firmware, are known to have unreliable UASP support. While I haven't seen it specifically mentioned, the INIC-3609 may be one of those chips.
The three USB 3.0 controller cards all have Renesas uPD720201 chips. Each card is from a different controller card manufacturer. The three computers used for testing are all using the Renesas 3.23.0 driver, although they all have different Windows versions (7 64-bit, 2003 64-bit, and XP 32-bit). Renesas claimed in press releases in 2011 and 2013 that their driver supports UASP in XP, Vista, and 7 via driver code from Media Logic. INIC-3609 also supports UASP, so I am assuming UASP is active. I would like to try disabling UASP (revert to BOT mode) on either the bridge or the driver. I've contacted Initio, but they haven't updated their site in a couple of years and may be defunct. I'm waiting to hear back from Renesas as well.
I'm aware that in Widows 8/8.1/10 using the generic built-in driver and replacing uaspstor.sys with usbstor.sys is an effective means of disabling UASP on the Renesas controller, but since the PCs using the Seagate USB drives can't currently be upgraded to 8/8.1/10 it doesn't matter if that solution would work. Also, Microsoft may break the ability of that solution to work at any time in a future security or feature update, so it can't be considered a long-term solution.
Any additional help or suggestions would be welcome!